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Number of different pairs of primes p,q such that : p<(q-2), p is a twin prime of p-2 or p+2 and q is a twin prime of q-2 or q+2, 2*n=p+q
(history; published version)

#8 by Reinhard Zumkeller at Fri Mar 14 14:04:10 EDT 2014

STATUS

editing

approved

#7 by Reinhard Zumkeller at Thu Mar 13 17:17:52 EDT 2014

PROG

(Haskell)

a159700 n = length $ filter (\(p, q) -> p < q - 2 && a164292 q == 1) $

zip ps (map (2 * n -) ps)

where ps = filter ((== 1) . a164292) [1..n]

-- Reinhard Zumkeller, Mar 13 2014

CROSSREFS

Cf. A164292.

STATUS

approved

editing

#6 by Reinhard Zumkeller at Tue Jan 28 00:52:06 EST 2014

STATUS

editing

approved

#5 by Reinhard Zumkeller at Tue Jan 28 00:36:34 EST 2014

KEYWORD

nonn,look

STATUS

approved

editing

#4 by Russ Cox at Sat Mar 31 13:22:06 EDT 2012

AUTHOR

_Pierre CAMI (pierre-cami(AT)bbox.fr), _, Apr 20 2009

Discussion

Sat Mar 31

13:22

OEIS Server: https://oeis.org/edit/global/885

#3 by Charles R Greathouse IV at Mon Jul 11 12:56:39 EDT 2011

AUTHOR

Pierre CAMI (pierre-cami(AT)orangebbox.fr), Apr 20 2009

Discussion

Mon Jul 11

12:56

OEIS Server: https://oeis.org/edit/global/95

#2 by N. J. A. Sloane at Thu Nov 11 07:34:06 EST 2010

LINKS

Pierre CAMI, <a href="/A159700/b159700.txt">Table of n, a(n) for n=1..50000</a>

KEYWORD

nonn,new

nonn

#1 by N. J. A. Sloane at Tue Jun 01 03:00:00 EDT 2010

NAME

Number of different pairs of primes p,q such that : p<(q-2), p is a twin prime of p-2 or p+2 and q is a twin prime of q-2 or q+2, 2*n=p+q

DATA

0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 3, 4, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 4, 3, 3, 4, 2, 1, 2, 1, 2, 4, 2, 0, 0, 0, 2, 4, 3, 2, 2, 2, 4, 6, 3, 2, 4, 2, 1, 2, 1, 2, 4, 2, 1, 2, 2, 3, 4, 2, 2, 4, 3, 3, 4, 2, 2, 4, 2, 3, 6, 3, 1, 2, 1, 3, 6, 4, 2, 2, 1, 2, 4, 3, 4, 6, 4, 3, 4, 2, 6, 12

OFFSET

1,8

COMMENTS

conjecture : for n>2104 there is at least one such pair of primes p+q=2*n

LINKS

Pierre CAMI, <a href="b159700.txt">Table of n, a(n) for n=1..50000</a>

EXAMPLE

3+13=16,5+11=16 so for n=8 2 pairs p,q such that p+q=2*8, p<(q-2) p and q have a twin prime

KEYWORD

nonn

AUTHOR

Pierre CAMI (pierre-cami(AT)orange.fr), Apr 20 2009

STATUS

approved